The number of values of $k$ for which the equation $x^2 - 3x + k = 0$ has two real and distinct roots lying in the interval $(0, 1)$ is

If $f(x) = \frac{1}{4x^2 + 2x + 1}$,then its maximum value is

If $f:[1, 2] \rightarrow R$ defined by $f(x) = x^2 + 2kx + k$ is always negative for all $x \in [1, 2]$,then the interval in which $k$ lies is:

If $a, b, c$ are real numbers and $a > 0$,what is the minimum value of the quadratic expression $ax^2 + bx + c$ for real $x$?

Let $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$,where $x \in R$. If $b$ and $c$ are nonzero real numbers such that $\min f(x) > \max g(x)$,then $\left|\frac{c}{b}\right|$ lies in the interval:

If the roots of the quadratic equation $x^2 - 2kx + k^2 + k - 5 = 0$ are less than $5$,then in which interval does $k$ lie?